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Topological Methods In Group Theory

Author: Ross Geoghegan
Publisher: Springer Science & Business Media
ISBN: 0387746110
Size: 67.88 MB
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This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Geometric And Cohomological Group Theory

Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 131662322X
Size: 57.64 MB
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Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

Two Dimensional Homotopy And Combinatorial Group Theory

Author: Cynthia Hog-Angeloni
Publisher: Cambridge University Press
ISBN: 9780521447003
Size: 72.71 MB
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Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.

Applicable Differential Geometry

Author: M. Crampin
Publisher: Cambridge University Press
ISBN: 9780521231909
Size: 13.81 MB
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An introduction to geometrical topics used in applied mathematics and theoretical physics.

Synthetic Differential Geometry

Author: Anders Kock
Publisher: Cambridge University Press
ISBN: 0521687381
Size: 46.60 MB
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Second edition of this book detailing how limit processes can be represented algebraically.

Representation Theory Of Lie Groups

Author: M. F. Atiyah
Publisher: Cambridge University Press
ISBN: 0521226368
Size: 55.57 MB
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In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.

Algebraic Varieties

Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Size: 72.74 MB
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An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

General Theory Of Lie Groupoids And Lie Algebroids

Author: Kirill C. H. Mackenzie
Publisher: Cambridge University Press
ISBN: 0521499283
Size: 34.22 MB
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This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.